Pulse-Shape Analysis of PDM-QPSK Modulation Formats

for 100 and 200 Gb/s DWDM transmissions

Andrés Macho Ortiz · Paloma R.Horche

Abstract Advanced optical modulation format

polarization-division multiplexed quadrature phase shift

keying (PDM-QPSK) has become a key ingredient in the

design of 100 and 200-Gb/s dense wavelength-division

multiplexed (DWDM) networks. The performance of this

format varies according to the shape of the pulses

employed by the optical carrier: non-return to zero

(NRZ), return to zero (RZ) or carrier-suppressed return to

zero (CSRZ). In this paper we analyze the tolerance of

PDM-QPSK to linear and nonlinear optical impairments:

amplified spontaneous emission (ASE) noise, crosstalk,

distortion by optical filtering, chromatic dispersion (CD),

polarization mode dispersion (PMD) and fiber Kerr

nonlinearities. RZ formats with a low duty cycle value

reduce pulse-to-pulse interaction obtaining a higher

tolerance to CD, PMD and intrachannel nonlinearities.

Keywords Modulation formats · Quadrature Phase Shift

Keying · duty cycle · spectral efficiency (SE) ·

intrachannel nonlinearities

1 Introduction

Nowadays, communication networks are required to

provide an enormous data transport capacity to solve the

continuous increase of internet traffic. The amount of

traffic carried on backbone networks has been growing

exponentially over the past two decades. The required

network bandwidth increases between 40% and 60% per

year due to the rapid emergence of new communication

services: social networking, 4K video, data traffic of

smartphones and tablets, and cloud services. The

explosion of these services has led to the necessity of

implementing new technologies in optical transport

networks which increase their capacity [1,2,3].

Since the 90s, traffic demand in core optical networks

has been covered by WDM systems, which have been

able to scale up their capacity from 10-Mb/s per channel

to 100-Gb/s at present [4]. Migration from 40 to 100-Gb/s

has not been so immediate because it has required

additional transmission techniques that would allow this

bit rate compatibility with DWDM-50 GHz grid.

Polarization-division multiplexing (PDM) was developed

to increase spectral efficiency of QPSK modulation

format from 2 b/s/Hz to 4 b/s/Hz. In addition, the use of

coherent detection, digital signal processing (DSP) and

forward error correction (FEC) techniques, the standard

100 Gigabit Ethernet (GbE) became a reality at the end of

2010 and at the beginning of 2011 [2]. With the impulse

and development of Cloud Computing, the capacity

offered by DWDM networks could be short in the next

years, so optical communications should survey beyond

100-G, being the next step the standard 400 GbE,

estimated for the year 2016 [3,5,6].

A.Macho ∙ P.R.Horche ( ) Departamento de Tecnología Fotónica y Bioingeniería

Escuela Técnica Superior de Ingenieros de Telecomunicación

Universidad Politécnica de Madrid, Avda. Complutense nº30

28040 Madrid, Spain

A.Macho

e-mail: macho.andres@tfo.upm.es

telephone: +34649994228

P.R.Horche

e-mail: phorche@tfo.upm.es

telephone: +34913367306

fax: +34913367319

As previous step to the 400 GbE, the immediate

necessity is to migrate from 100-G to 200-G. To achieve

this bit rate is likely to continue initially with the parallel

transmissions approach: 5 parallel lanes of 40-Gb/s or 2

parallel lanes with quickly maturing 100-Gb/s technology,

[3]. But the tendency is to integrate 200-Gb/s in 50 GHz

grid through a single lane.

Therefore, high spectral-efficiency (S.E) PDM-M-

QAM formats have been proposed to increase the S.E

beyond 4 b/s/Hz. The main drawback of using dense

digital constellations is their high vulnerability to the

nonlinear effects of the optical fiber, increasing the

system complexity to achieve long-haul transmissions

with these formats [7]. The other disadvantage inherent to

the use of dense digital constellations is that it would be

necessary a higher resolution in the analogic-to-digital

(ADC) converters of the coherent receiver [8].

Due to the difficulties to obtain long-haul optical

transmissions with PDM-M-QAM formats [9], the

International Telecommunication Union Standardization

Sector (ITU-T) has enabled to leave the rigid grid of 50

GHz in 2012 with the proposal of flexible DWDM

networks [10]. In this way, it is possible to avoid the use

of PDM-M-QAM formats employing 200G-PDM-QPSK

signals with 100 GHz between optical carriers (Fig. 1).

For the integration in DWDM-50 GHz grid it is being

studied the Nyquist filtering approach (N-WDM), which

reduces the width of the main spectral lobe [11] at the

expense of a strong filtering distortion. This penalty could

be solved with Maximum-Likelihood Sequence Detection

(MLSD) [12,13]. However, the abrupt transition band of

Nyquist filtering is currently far from its implementation,

so the practical approach is to use these formats over the

grid of 100 GHz for 200-Gb/s transmissions.

The performance of PDM-(D)QPSK varies according

to the line code that is employed over the pulses of the

optical carrier. The question as to the ‘best’ optical

modulation format cannot be concluded until the pulse is

fully shaped: NRZ, RZ or CSRZ (Table 1). Each of the

options offers different tolerances to linear and nonlinear

optical impairments:

ASE noise

Crosstalk and optical filtering distortion

Chromatic dispersion

PMD

Fiber Kerr Nonlinearities

In this paper we will analyze the features of PDM-

(D)QPSK in 100 and 200-Gb/s transmissions heeding the

above physical impairments. The paper is organized as

follows. Section II presents the architecture of the

simulation scenario and its main parameters, in Section

III is investigated the ASE noise tolerance, in Section IV

is analyzed the crosstalk and optical filtering distortion,

Section V is devoted to chromatic dispersion, Section VI

measures the robustness of these formats to PMD, in

Section VII the nonlinear regime is analyzed, and finally

Section VIII concludes this paper.

2 Simulation scenario

The simulations have been performed with

computational-aided design tool OptiSystem. The

analysis of PDM-(D)QPSK depends largely each of the

devices that make up the optical network, so that the

results will be subject to the simulation scenario. For this

reason the simulations of the next sections have been

implemented over a generic model of DWDM network

(Fig. 2) [14]. The system includes 16 wavelengths (32

optical channels due to PDM). For 100 and 200-Gb/s

transmissions the spectral separation between super-

channels is 50 and 100 GHz respectively. The frequency

bands are 192.75 ‒ 193.5 THz in the first case and 192.4 ‒

193.9 THz in the second case. Transmission is performed

in 6x100-km spans with EDFA amplification. We have

Modulation Formats

100/200-Gbps

PDM-NRZ-(D)QPSK

PDM-67%RZ-(D)QPSK

PDM-50%RZ-(D)QPSK

PDM-33%RZ-(D)QPSK

PDM-CSRZ-(D)QPSK

Table 1 Different pulse shapes in PDM-(D)QPSK modulation.

Fig. 1. PDM-(D)QPSK modulation formats for 100 and 200-Gb/s

transmissions in DWDM systems.

employed standard single-mode fiber (SSMF) or non-zero

dispersion shifted fiber (NZDSF+) depending on the

simulation implemented on each section. The main fiber

parameters are shown in Table 8. We have included in the

optical link two multiplexers, two demultiplexers, a

reconfigurable optical add-drop multiplexer (ROADM)

and some optical filters to characterize the simulation

scenario as realistically as possible. In each optical

impairment discussed, the simulated scenario will have

slight variations, but all of them share some general

parameters (Table 2).

During the next sections the performance of PDM-

(D)QPSK will be analyzed in the presence of the main

physical impairments. The tolerance to ASE noise,

crosstalk, optical filtering, chromatic dispersion, PMD

and nonlinearities will be studied in order to discover the

pulse-shape (NRZ, RZ or CSRZ) which provides the best

performance in DWDM networks. QPSK and DQPSK

have the same temporal and spectral profile, so the

results of the analysis will be identical for both formats.

We will refer to these two modulations under the joint

notation of (D)QPSK. The only difference between them

is that QPSK carries the information into the phase of

optical pulses but DQPSK encodes the digital symbols

into the phase transitions.

3 ASE noise tolerance

Essential mechanisms of power losses in an optical fiber

are mainly derivatives of the absorption, spatial

dispersion and power radiated to the cladding [15]. In

long-haul transmissions, optical systems require optical

amplification because fiber losses reduce the signal power

below the detectability threshold of photodetectors.

Optical amplifiers can be designed as lumped elements

periodically spaced through the link forming several

amplification spans typically spaced 80 to 100 km in

terrestrial systems and 40 to 60 km in submarine

transmissions [2,15]. Optical amplification can also be

distributed by introducing gain along the transmission

fiber.

The main drawback of optical amplifiers in a

multispan scenario is the generation and accumulation of

amplified spontaneous emission (ASE) noise in the

optical spectrum. If multiple optical amplifiers are

concatenated to periodically compensate for fiber loss,

ASE builds up in the system, in analogy to the noise

build-up in an electrical amplifier chain. This noise build-

up is captured by the optical signal-to-noise ratio

(OSNR), which degrades with every amplifier along the

propagation path [16,17].

The ASE noise tolerance of 100 and 200-Gb/s PDM-

(D)QPSK signals is fully characterized by the required

OSNR (OSNRreq) [1], which is the OSNR that is needed

to achieve a specified target BER. Excluding FEC

overhead, the OSNRreq for a BERref = 10-12 was calculated

in a single-channel back-to-back (B2B) scheme, where

the transmitter is directly connected to the synchronous

homodyne coherent receiver [18,19], without filters or

optical fiber between TX and RX (Fig. 2). The goal is to

discover the pulse-shape (NRZ, RZ or CSRZ) that offers

better sensitivity. A higher sensitivity ensures greater

tolerance to degradation by accumulation of ASE noise in

the spectrum. Table 3 gives the results obtained in this

Parameter

Value

Laser linewidth (ECL)

100 KHz

MZM extinction ratio

30 dB

Noise Figure (EDFA)

5 dB

Dark Current (PIN)

10 nA

Responsivity (PIN)

0,9 A/W

Thermal noise

1x10-22 W/Hz

Bandwidth in optical filters

(Second-order Gaussian filters)

43 GHz (50 GHz grid)

85 GHz (100 GHz grid)

RF filters

Fourth-order Bessel filters

Cutoff frequency

0,75 x Rs

PRBS-Sequence length

32768 bits

Table 2 General parameters of the simulation scenario.

Fig. 2. Generic setup of a WDM system with polarization division multiplexing (PBC-Polarization Beam Combiner, PBS-Polarization

Beam Splitter).

Modulation Format

Coherent Detection

OSNRreq

(BERref=10-12)

100 Gb/s

OSNRreq

(BERref=10-12)

200 Gb/s

PDM-NRZ-(D)QPSK

21,0 dB

24,9 dB

PDM-67%RZ-(D)QPSK

20,3 dB

24,2 dB

PDM-50%RZ-(D)QPSK

20,2 dB

24,1 dB

PDM-33%RZ-(D)QPSK

19,8 dB

23,7 dB

PDM-CSRZ-(D)QPSK

20,2 dB

24,1 dB

Table 3 Sensitivity of PDM-(D)QPSK signals (0.1-nm resolution

bandwidth).

section. These values may differ from other works cited

in the bibliography due to various optical and electronic

hardware implementation aspects, including drive

waveforms, filter characteristics and modulator extinction

ratio [4,16,20]. Nevertheless, there are some general facts

which are worth mentioning.

QPSK and DQPSK, which are multilevel modulations,

require only 0.5-dB more OSNR than PSK and DPSK

signals in coherent and differential interferometric

detection [20,21]. Leaving aside TX/RX complexity

aspects, the good OSNR performance makes PDM-

(D)QPSK an attractive candidate for optically routed

networks that require a trade-off between sensitivity and

spectral efficiency. OSNR values listed in Table 3 haven

been measured in both polarizations and in a 12.5-GHz

optical reference bandwidth.

RZ pulses require ~1 dB less OSNR for identical BER

than NRZ. Particularly, signals with a low duty cycle

require less OSNR to obtain the specified target BER.

The shorter the pulse width, the higher the sensitivity of

PDM-(D)QPSK. We can see in Table 3 that a reduction in

the duty cycle decreases OSNRreq in the modulation

format. Consequently, PDM-33%RZ-(D)QPSK ends

emerging as the option that offers the best sensitivity. In

contrast, NRZ version has the lowest sensitivity with 21-

dB and 25-dB in 100 and 200-Gb/s transmissions,

respectively.

On the other hand, with PDM-CSRZ-(D)QPSK we

can achieve a sensitivity similar to PDM-50%RZ-

(D)QPSK with a higher duty cycle (67%). This is mostly

due to the reduced impact of ISI over the CSRZ pulses.

4 Crosstalk, optical filtering and spectral efficiency

Some formats are better suited than others when it comes

to tight WDM channel packing, quantified by its spectral

efficiency. Apart from important SE-dependent

nonlinearity considerations, in DWDM networks with

high spectral efficiency there are two concern

impairments arising from dense WDM channel spacing:

crosstalk and filter narrowing.

An optical channel can be affected by two different

types of crosstalk [19]: linear or interchannel crosstalk

(undesirable power of adjacent DWDM channels in the

desired band generating interferences at square-law

detection) and homodyne or intrachannel crosstalk (also

known as Multipath Interference or MPI [20], which

describes the coherent interference of a signal with

residual signals at the same wavelength due to imperfect,

reflective fiber connectors, double-Rayleigh

backscattering, or due to from imperfect drop capabilities

of OADMs…). The former is quite easy to avoid with

optimal filtering of the desired band, but the latter is

hardly removed by optical filters.

In general, phase modulated signals are more tolerant

to linear and homodyne crosstalk than intensity

modulations [21,22]. In analogy to linear crosstalk,

undesirable power in-band with the signal gives rise to

signal-MPI beat noise at square-law detection becoming

amplitude jitter in the eye diagram, so that the eye

penalty in PDM-(D)QPSK is lower than in OOK signals

due to the information is encoded in the optical phase.

Strictly, the impact of crosstalk on system performance

depends on the number of interferers, the OSNR

delivered, the modulation format and the signals

waveform (in particular the signal extinction ratio, and

the phase coherence of the interfering signals).

The tolerance of PDM-(D)QPSK to linear and

homodyne crosstalk has been analyzed. We have

compared different pulse shapes affected by the same

crosstalk ratio and we do not find major differences

between them. The narrowband PDM-NRZ-(D)QPSK

signal is less susceptible to generate linear crosstalk

penalties. Meanwhile, a broadband modulation spectrum

is less susceptible to MPI penalties due to reduced signal-

MPI beat noise (RZ formats) [20].

On the other hand, in order to narrow the bandwidth

of 100 and 200-Gb/s PDM-(D)QPSK signals, it is

necessary to filter them with the optimal bandpass to

avoid crosstalk impairments. However, the main problem

of optical filtering appears in DWDM networks with

high spectral efficiency, where the concatenation of

multiple ROADM’s narrows the overall optical filter

bandwidth and distorts the signals. In this situation, it is

particularly relevant to analyze the tolerance of PDM-

(D)QPSK to filtering distortion.

In order to simulate realistic conditions, the set of

network devices with filters in their architectures (mux,

demux, ROADM's ...) is modeled as an equivalent

cascade of filters between TX and RX in a B2B scenario.

We have analyzed two different cases:

a) 100-Gb/s in DWDM 50-GHz grid: five second-order

Gaussian bandpass filters with Full-Width at Half-

Maximum (FWHM) bandwidth of 43 GHz.

b) 200-Gb/s in DWDM 100-GHz grid: five second-order

Gaussian bandpass filters with FWHM bandwidth of

85 GHz.

The FWHM value is specified by ITU-T in the Rec.

G.694.1 (2012) for DWDM systems [10]. To quantify

filtering distortion we have measured the sensitivity of

these new schemes for a BERref = 10-12 and then we have

compared the results with the sensitivities of Table 3.

The values of this analysis are reported in Table 4.

In general, modulation formats with a narrower

bandwidth are more tolerant to optical filtering

distortion. Minimum distortion is shown in PDM-NRZ-

(D)QPSK signal with a 0.9-dB penalty in the OSNRreq.

The higher the pulse temporal width, the smaller the

spectral width of the signal, and therefore there will be a

lower penalty in the OSNR by optical filtering.

Accordingly, the tolerance to filtering distortion of PDM-

(D)QPSK is directly proportional to the value of the duty

cycle. These affirmations can easily be tested with the

results measured: if we increase the duty cycle value in

the optical carrier, filtering distortion decreases and the

OSNR penalty reaches its minimum value for the NRZ

pulses.

Particularly notable is the survey of PDM-33%RZ-

(D)QPSK. This signal has half of SE in DWDM systems

(1 b/s/Hz), making it impossible to use in filterless

optical networks [14]. Nevertheless, the distortion in its

waveform by the above filters is not excessively high.

This feature will prove to be essential. The handicap of

RZ pulses with a low duty cycle is an insufficient SE (<

2 b/s/Hz). However, prefiltering these signals in the TX,

the SE can be increased to 2 b/s/Hz (Table 5) with a

minimal penalty of ~1 dB in the OSNR (Table 4).

Figure 3 shows the eye diagram of PDM-33%RZ-

(D)QPSK. It is just mildly distorted at the output of the

filters chain. Filtering distortion results only in a slight

amplitude and phase jitter quantified in 1.3-dB OSNR

penalty. With 50% RZ and CSRZ PDM-(D)QPSK, the

spectral width of the main lobe ranges between 50% and

80% of bit rate, so these modulations can be considered

as narrowband signals for the above filters. Hence, the

OSNR penalty is so low (≈1 dB).

5 Chromatic dispersion (CD)

Chromatic dispersion is a major impairment in high-

capacity optical transmission systems. The spectral

components of the optical signal have different group

velocities, so that they reach the end of the fiber with

different group delays [23,24]. Consequently, chromatic

dispersion (also called Group Velocity Dispersion –

GVD) results in the time domain in dispersive pulse

broadening. Dispersion in optical fiber is an all-pass filter

on the electric field of the lightwave, given by a complex

Modulation Format

OSNRreq

(BERref=10-12)

Penalty OSNR

(Ref: table III)

100-Gb/s

200-Gb/s

PDM-NRZ-(D)QPSK

21,9 dB

25,8 dB

+0,9 dB

PDM-67%RZ-(D)QPSK

21,3 dB

25,2 dB

+1,0 dB

PDM-50%RZ-(D)QPSK

21,4 dB

25,3 dB

+1,2 dB

PDM-33%RZ-(D)QPSK

21,0 dB

25,0 dB

+1,3 dB

PDM-CSRZ-(D)QPSK

21,3 dB

25,2 dB

+1,1 dB

Table 4 Tolerance to optical filtering (0.1-nm resolution bandwidth).

Modulation Format

SEWDM

w/o filtering

(b/s/Hz)

SEWDM

with filtering

(b/s/Hz)

PDM-NRZ-(D)QPSK

2

2

PDM-67%RZ-(D)QPSK

1,87

2

PDM-50%RZ-(D)QPSK

1,25

2

PDM-33%RZ-(D)QPSK

1

2

PDM-CSRZ-(D)QPSK

1,54

2

Table 5 Bandwidth and SE of PDM-(D)QPSK in 100 and 200-Gb/s

DWDM transmissions.

Fig. 3. (a)-(b) Spectrum and eye diagram of PDM-33%RZ-(D)QPSK

without filtering. (c)-(d) Spectrum and eye diagram of PDM-33%RZ-

(D)QPSK with prefiltering. The distortion in the waveform of this signal by optical filtering is not excessively high, ~1 dB OSNR

penalty.

transfer function which shows a quadratic dependence in

its complex phase with the instantaneous frequency, like

a chirp filter. CD produces a variation of the

instantaneous frequency in a modulated optical signal

[25]. This variation of the instantaneous frequency

results in pulse broadening which generates inter-symbol

interference (ISI). Obviously, after propagating some

distance in the fiber, a point is reached where the

accumulating pulse spread is too great for the receiver to

recover the signal pulses within the equipment BER

specifications.

Table 6 quantifies the accumulated chromatic

dispersion (CDacum) required to induce a 2-dB penalty in

the OSNR at 200-Gb/s transmissions (100-Gb/s results

have been excluded due to space limitations). Obviously,

those signals that require more CDacum to reach the 2-dB

penalty show better tolerance to this impairment. The

second column presents the CD tolerance in filterless

optical networks [14], without optical filtering in the

simulation scenario (Fig. 2) and the third column

assumes the presence of filters. An optical filter disturbs

the waveform and the spectrum of the signals, so that the

tolerance to CD will also be affected. Currently, optical

networks have many devices with filtering in their

architectures so this analysis should be performed.

Graphs 4 and 5 also reflect the tolerance differences

to CD between PDM-(D)QPSK signals. We can see the

OSNR penalty evolution as a function of CDacum for each

signal, so that it is relatively simple to check out the

formats that are more tolerant to CD with and without

optical filtering in the simulation scenario. Attenuation,

PMD and fiber nonlinearities have been disabled in the

simulation scheme (Fig. 2) to measure the OSNR penalty

exclusively due to CDacum. Nonlinearities, like filtering,

may also modify the dispersion tolerance: SPM and

XPM broaden the bandwidth of the signals and hence

their ability to resist the CD. Nevertheless, intrachannel

nonlinearities prevail over interchannel nonlinear effects

in WDM systems beyond 40-Gbps/channel, so the results

listed in Table 6 are quite similar with and without Kerr

effect enabled. SSMF and NZDSF+ fibers have been

employed to measure the tolerance to CD as objectively

as possible (fiber parameters in Table 8). In addition, to

include the CD analysis in presence of optical filters in

the simulation scenario, five second-order Gaussian

Modulation Format

CDacum

w/o filtering

[ps/nm]

(2-dB pen.)

CDacum

FWHM = 85 GHz

[ps/nm]

(2-dB pen.)

PDM-NRZ-(D)QPSK

67,8

91,5

PDM-67%RZ-(D)QPSK

56,4

93,2

PDM-50%RZ-(D)QPSK

54,6

95,0

PDM-33%RZ-(D)QPSK

52,0

95,1

PDM-CSRZ-(D)QPSK

49,3

94,0

Table 6 Tolerance to chromatic dispersion for 200 Gb/s transmissions.

Fig. 4. OSNR penalty as a function of CDacum (ps/nm) without optical

filtering.

Fig. 5. OSNR penalty as a function of CDacum (ps/nm) with optical filtering.

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

OS

NR

Pen

alt

y (

dB

)

CDacum (ps/nm)

CD Tolerance (w/o filtering)

PDM-NRZ-(D)QPSK

PDM-33% RZ-(D)QPSK

PDM-50% RZ-(D)QPSK

PDM-67% RZ-(D)QPSK

PDM-CSRZ-(D)QPSK

1

1.5

2

2.5

3

3.5

4

4.5

5

70 80 90 100 110 120 130 140

OS

NR

Pen

alt

y (

dB

)

CDacum (ps/nm)

CD Tolerance (with filtering)

PDM-NRZ-(D)QPSK

PDM-33% RZ-(D)QPSK

PDM-50% RZ-(D)QPSK

PDM-67% RZ-(D)QPSK

PDM-CSRZ-(D)QPSK

bandpass filters were added with the same configuration

as in the previous section.

The tolerance of a modulation format to CD with and

without filtering is fixed by the spectrum and the

waveform launched to the fiber. In a simulation scenario

without optical filters these factors are exclusive of the

specific modulation employed in the lightpath. In

contrast, in the scenario with filtering the waveform and

the spectrum are determined by the set “modulation &

filters”. The narrower the signal spectrum, the higher the

tolerance to the CDacum. Filtering process reduces the

bandwidth of the signals, so the difference between the

group delays of the different spectral components will be

smaller.

In the simulation without filtering (the second column

of Table 6 and Fig. 4), the signals with more duty cycle

have a narrower spectrum, so PDM-NRZ-(D)QPSK and

PDM-67%RZ-(D)QPSK are the most tolerant to

chromatic dispersion. In contrast, 33% RZ and CSRZ

pulses present the worst performance. Particularly, PDM-

CSRZ-(D)QPSK, with the optical carrier suppressed, will

have better tolerance to fiber nonlinearities but this signal

loses robustness against accumulated chromatic

dispersion, as same as CSRZ-OOK format [20]. Despite

occupying a lower bandwidth than PDM-33%RZ-

(D)QPSK, the CSRZ version has the worst tolerance to

CD.

On the other hand, the order of the tolerance to CD

between the different versions is reversed with optical

filtering. As can be seen in the third column of Table 6

and Fig. 5, whereas PDM-NRZ-(D)QPSK shows more

resilience to CD than RZ versions in absence of filters,

PDM-RZ-(D)QPSK signals are more robust to CD in

presence of filters in the network. Filters guarantee

identical bandwidths in PDM-(D)QPSK formats, so that

CD tolerances are similar (the difference between the

group delays of the spectral components hardly vary

from one signal to another). Under identical conditions of

spectral width, the modulation with the narrowest

Gaussian pulses will show more robustness to CD. ISI

will be lower than in high duty cycle pulses for the same

CDacum value, so that PDM-33%RZ-(D)QPSK will have

the most resilience to CD in this case.

Prefiltering PDM-RZ-(D)QPSK formats it is possible

to increase their SE to 2 b/s/Hz in DWDM systems and

their tolerance to chromatic dispersion. Prefiltering

reduces the spectral components, so the difference

between the group delays is also reduced. Consequently,

the CD tolerance is increased. This feature is essential to

understand in Section 7 the great tolerance of this format

to intrachannel fiber Kerr nonlinearities, where the

chromatic dispersion plays a fundamental role.

6 Polarization mode dispersion

In ideal single-mode fibers, the two orthogonal modes

that compose the fundamental mode LP01 would be

degenerated with identical propagation properties

because they would have the same cutoff frequency and

the same propagation constant.

However, in real single-mode fibers, minute

waveguide asymmetries, either due to manufacturing

imperfections or due to stress imposed by mechanical

vibrations or temperature variations, the circular

symmetry between the core and cladding is not perfect

[26]. Under these conditions the two orthogonal modes

are non-degenerate. They have the same cutoff frequency

but their propagation constants are slightly different,

exhibiting different group velocities, and giving rise to a

Differential Group Delay (DGD) [15,27]. Because of the

difference between the group delays of both

polarizations, the initial pulse is broadened: After square-

law detection, the electrical signal is given by the

quadratic sum of both polarizations [20]:

𝑆(𝑡) = |𝐸𝑥(𝑡)|2 + |𝐸𝑦(𝑡 − 𝐷𝐺𝐷)|

2 (1)

This phenomenon is called Polarization Mode

Dispersion (PMD). If the DGD parameter is constant

over wavelength, it is referred to first-order PMD and it

predominates over superior PMD orders for many

applications. The DGD can be considered constant across

a single WDM channel, so the first-order PMD has been

studied in a single-channel transmission. The simulation

scenario is the same as Fig. 2 with only one TX/RX

(193.1 THz channel). A PMD emulator was added

between the TX and the RX. Table 7 and Figure 6 have

been obtained varying the DGD parameter in the PMD

emulator.

Table 7 quantifies the first order PMD tolerance of

PDM-(D)QPSK formats in 100 and 200-Gb/s

transmissions. It shows the DGD that leads to a 1-dB

Modulation Format

DGD-100Gb/s

(1-dB pen.)

DGD-200Gb/s

(1-dB pen.)

PDM-NRZ-(D)QPSK

19,0 ps

7,9 ps

PDM-67% RZ-(D)QPSK

19,4 ps

8,2 ps

PDM-50% RZ-(D)QPSK

19,6 ps

8,4 ps

PDM-33% RZ-(D)QPSK

20,0 ps

8,6 ps

PDM-CSRZ-(D)QPSK

19,6 ps

8,4 ps

Table 7 First-order PMD tolerance. It shows the DGD (ps) that leads

to a 1-dB OSNR penalty.

OSNR penalty. The first-order PMD tolerance of a

modulation format is linear with the symbol period [28].

For most of them, a 1-dB penalty occurs at a DGD value

between 30% and 40% of the symbol period. The

tolerance of PDM-(D)QPSK formats is very similar and

there are no major differences between them, with RZ

formats being in general more resilient to PMD than the

NRZ version.

The worst result is observed using the NRZ pulses.

The Non-Return to Zero pulses, occupying the entire

symbol interval, overlap each other with a lower DGD

between polarizations. In contrast, PDM-33%RZ-

(D)QPSK is the most resilient to PMD (DGDMAX). The

reason is simple: the narrower the RZ pulses, the higher

DGD required to overlap adjacent pulses with the same

ISI-penalty. Therefore, PDM-33%RZ-(D)QPSK requires

a higher DGD between polarizations to suffer the same

OSNR penalty as pulses with more duty cycle.

Meanwhile, PDM-CSRZ-(D)QPSK shows the same

tolerance to first-order PMD as a 50% RZ despite having

a 67% duty cycle value.

Additionally, Fig. 6 shows the OSNR penalty as a

function of DGD for 200G-PDM-(D)QPSK signals (100-

Gb/s results are not included due to space limitations, but

the order of the tolerances to PMD between 100G-PDM-

(D)QPSK formats remains unalterable). It is also obvious

that the signal with the lowest duty cycle is the most

robust to PMD.

On the other hand, note that the resilience to PMD, in

addition, depends to an appreciable extent on the

waveforms and filters as well as other residual distortions

such as CD and fiber Kerr nonlinearities [19].

7 Fiber Kerr nonlinearities

The effective area of a single-mode fiber typically ranges

between 20 and 100 μm2 resulting in a strong

confinement of the light within the fiber core, so that the

optical intensity can easily exceed MW/cm2. Due to the

presence of an optical intensity so high, the refractive

index value could be affected resulting in a phase

deviation of the fundamental mode. The refractive index

dependence with the optical intensity is known as the

Kerr effect [29].

In order to better understand the origin of

nonlinearities, the Kerr effect can be classified into more

specific nonlinear interactions that can distort optical

signals in different ways (Fig. 7). Fiber nonlinearities

occurring between pulses of the same WDM channel are

referred to as intrachannel nonlinearities and the

nonlinearities occurring among two or more WDM

channels, the expression interchannel nonlinearities is

used [28].

The nonlinear regime of a single-polarization

electrical field through a single-mode optical fiber is

described by the Generalized Nonlinear Schrödinger

Equation (GNLSE) [20,24,29]:

𝜕�⃗� 1(𝑧, 𝑡)

𝜕𝑧+𝑗

2𝛽2(𝑧)

𝜕2�⃗� 1(𝑧, 𝑡)

𝜕𝑡2−1

6𝛽3(𝑧)

𝜕3�⃗� 1(𝑧, 𝑡)

𝜕𝑡3+

+𝛼(𝑧)

2�⃗� 1(𝑧, 𝑡) = 𝑗𝛾|�⃗� 1|

2�⃗� 1⏟

𝑺𝑷𝑴−𝑰𝑺𝑷𝑴

+ 2𝑗𝛾 {|�⃗� 2|2+ |�⃗� 3|

2} �⃗� 1⏟

𝑿𝑷𝑴−𝑰𝑿𝑷𝑴

+

+ 𝑗𝛾�⃗� 1�⃗� 2�⃗� 3∗ ⏟

𝑭𝑾𝑴−𝑰𝑭𝑾𝑴

(2)

In intrachannel nonlinearities E⃗⃗ 1, E⃗⃗ 2 and E⃗⃗ 3 represent

the electric fields associated to three different optical

pulses from the same WDM channel, meanwhile they

represent three different WDM channels in interchannel

nonlinearities.

The nonlinear interaction of a channel or a pulse with

itself is referred to as self-phase modulation (SPM).

Whether SPM relates to an entire channel or an isolated

pulse (ISPM) depends on the context [19]. ISPM

explains the phase variations in E⃗⃗ 1 which are generated

by fluctuations in its own intensity, considering the

isolated pulse and without the intervention of adjacent

pulses [20]. The intensity variations in E⃗⃗ 1 cause changes

Fig. 6. OSNR penalty as a function of DGD [ps].

0.5

1

1.5

2

2.5

3

6 7 8 9 10 11 12 13 14 15 16 17 18

OS

NR

Pen

alt

y (

dB

)

DGD (ps)

PMD Tolerance

PDM-NRZ-(D)QPSK

PDM-33% RZ-(D)QPSK

PDM-50% RZ-(D)QPSK

PDM-67% RZ-(D)QPSK

PDM-CSRZ-(D)QPSK

in the refractive index resulting in variations in its own

phase.

Intrachannel cross-phase modulation (IXPM) and

intrachannel four-wave mixing (IFWM) are the others

intrachannel nonlinearities arising from the signal-signal

interactions. They are the dominant nonlinear effects

beyond 40-Gb/s per channel transmissions. Both

phenomena are generated as a result of the overlapping

between pulses in a single optical carrier due to CD at the

same time that the Kerr effect is being stimulated

[19,30]. IXPM explains the pulse phase variations due to

intensity fluctuations in the overlapped adjacent pulses.

On the other hand, IFWM explains the interaction

between three different pulses within the same optical

channel. The pulses interaction generates a fourth pulse

with random amplitude, often referred as ghost pulse

[19,28]. The IXPM effects can be visualized in the eye

diagram as phase jitter while IFWM generates amplitude

jitter. In Fig. 8 both concepts can be visualized.

The intensity fluctuations generated by ASE noise

and adhered over the pulse amplitude are potentially

hazardous in presence of SPM. They induce random

phase fluctuations (signal-ASE interactions). This phase

jitter is a new noise known as nonlinear phase noise

(NPN), also referred as the Gordon-Mollenauer effect

[17,19,28,31] and it is particularly detrimental for phase-

modulated systems between 1 and 20-Gb/s. Beyond 40-

Gb/s, the Gordon-Mollenauer effect is not an important

nonlinear impairment [21], although optical signals are

affected by NPN from intrachannel nonlinearities due to

signal-ASE interactions. NPN is especially detrimental in

dispersion managed (DM) systems with phase-modulated

signals.

Two new phenomena appear associated with signal-

signal interactions in interchannel nonlinearities: cross-

phase modulation (XPM) and four-wave mixing (FWM)

[29]. These nonlinear effects are assumed widely known

so they are not described in this paper.

The easiest way to reduce the XPM effects is

increasing the spectral separation between optical

carriers or using optical fibers with a higher chromatic

dispersion coefficient to avoid the spatial overlap

between pulses of different WDM channels [15,32].

Beyond 20-Gb/s, XPM is not an important impairment in

nonlinear regime [28,29]. Considering the signal-ASE

interaction, XPM can induce NPN in adjacent channels.

In contrast with the Gordon-Mollenauer effect, NPN

induced by XPM cannot be compensated because it is not

correlated with the received optical intensity [19],

although its impact in the OSNR is lower than the

Gordon-Mollenauer effect in SSMF fibers in 10-Gb/s

systems [21]. A major consequence of SPM and XPM

(signal-signal and signal-ASE interactions) is the spectral

broadening of the pulses that increases the channels

bandwidth considerably and limits the performance of a

lightwave system [25]. Therefore, both phenomena

contribute to reduce the system tolerance to chromatic

dispersion [28].

On the other hand, FWM is generated, like XPM, due

to the nonlinear response of the dielectric polarization

with the electric field of the light. Nevertheless, FWM

will cease to be a source of degradation in the nonlinear

regime beyond 80-Gb/s transmissions [21,32]. According

to Winzer’s studies [20,21,28,31], intrachannel

nonlinearities only prevail beyond 40-Gb/s per channel

transmissions: IFWM in SSMF spans and IXPM in

NZDSF+ spans. Beyond 200-Gb/s, IFWM is the major

impairment in the nonlinear regime.

Fig. 7. Classification of Kerr nonlinearities.

Fig. 8. Effects of IXPM and IFWM on a 100 and 200-Gb/s PDM-

(D)QPSK signals. The upper graphs show the signal waveform after

transmission. The lower graphs show the eye diagram. The main effect

of IXPM is to produce timing jitter, meanwhile IFWM induces amplitude jitter (ghost pulses).

7.1 IXPM and IFWM tolerance

The simulations of this section have been designed to

survey the tolerance of 100/200G-PDM-(D)QPSK

signals to IXPM and IFWM, the dominant nonlinearities

beyond 40-Gb/s. In this section, the simulations have

been supported on the DWDM system shown in Fig. 2.

The analysis in the nonlinear regime depends on many

parameters of the simulation scenario and its operating

conditions [33], so one should be very careful with the

measurements to obtain conclusions as objective as

possible. The presence of IXPM and IFWM is directly

related to the GVD coefficient of the fiber, so both

phenomena have been analyzed for SSMF and NZDSF+

spans (parameters in Table 8).

Firstly, we initially tested the absence of FWM and

XPM in 100 and 200-Gb/s transmissions. DWDM

spectrum was controlled along the lightpath, checking

that no new spectral components were generated (FWM

not found) and the bandwidth of each channel remained

unchanged (XPM not found) during the propagation.

These tests ensured that the predominant nonlinearities

were IXPM and IFWM for both types of fibers.

Afterwards, in Fig. 9, we calculated the OSNR

penalty evolution as a function of the power launched

into the fiber to find the pulse-shape that is the most

robust to IXPM and IFWM in PDM-(D)QPSK signals.

We only show the graph for the 200-Gbps-SSMF case

because the tolerance order to nonlinear regime among

the different pulses does not vary in the other analyzed

cases (NZDSF+ and 100-Gb/s). Although the graph for

the NZDSF+ has not been included due to space

limitations in this document, it is interesting to compare

with the SSMF in the nonlinear regime. The robustness

to nonlinearities can be increased using the standard

single-mode fiber [36] due to a higher CD coefficient, a

higher effective area and a lower nonlinear coefficient.

Attending to its CD coefficient, optical pulses will be

more broadened with a lower distance than in the

NZDSF+, so that the peak power of the temporal profile

of the pulses will drop before and they will propagate

fewer kilometers stimulating the Kerr effect [37]. For the

same value of Plaunch (dBm), the Kerr effect will be

stimulated in the SSMF spans during a shorter distance

than in NZDSF+ spans.

PDM-(D)QPSK signals exhibit an excellent tolerance

to intrachannel nonlinearities. In 100 and 200-Gb/s

transmissions, IFWM appears in the SSMF and NZDSF+

whereas IXPM is mainly stimulated in the NZDSF+. In

general, phase modulated signals are more robust to

IFWM than OOK formats because the relative phase

between pulses does not vanish and hence the ghost

pulses generated by IFWM have a lower amplitude.

33%-RZ and CSRZ pulses are the most tolerant to IFWM

and IXPM. Knowing that IFWM and IXPM arise from

pulse-to-pulse interactions, the shorter the pulse width,

the higher the tolerance to these phenomena [30,38].

With a low duty cycle, RZ pulses need more CDacum to

overlap with each other. In that case, there will be a

lower peak power in optical pulses with more CDacum, so

the Kerr effect will be less stimulated. Therefore, a

higher optical power will be necessary to launch into the

fiber to achieve the same OSNR penalty as in pulses with

a higher duty cycle. Accordingly to Fig. 9, the worst

tolerance to IFWM and IXPM is found in the PDM-

NRZ-(D)QPSK signal.

However, the high robustness offered by PDM-

CSRZ-(D)QPSK is nearly identical to the 33% RZ

version. A large resistance to nonlinearities is achieved

Optical Fiber

SSMF

NZDSF+

D [ps/(nm∙km)]

+17

+4

S [ps/(nm2∙km)]

+0.088

+0.084

ATH [dB]

0.2

0.2

Aeff [μm2]

80

72

n2 x10-20 [m2/W]

2.60

3.53

DPMD [ps/km1/2]

< 0.1

< 0.1

Table 8 Parameters of SSMF and NZDSF+ fibers [34,35].

Fig. 9. Tolerance to IXPM and IFWM. OSNR penalty as a function of

Plaunch (dBm).

0

1

2

3

4

5

4 5 6 7 8 9 10 11 12 13 14 15 16 17

OS

NR

Pen

alt

y (

dB

)

Plaunch (dBm)

IXPM and IFWM tolerance (200-Gb/s)

PDM-NRZ-(D)QPSK

PDM-33% RZ-(D)QPSK

PDM-50% RZ-(D)QPSK

PDM-67% RZ-(D)QPSK

PDM-CSRZ-(D)QPSK

suppressing the optical carrier in RZ pulses despite

having a higher duty cycle (67%).

7.2 Variation of IXPM and IFWM with the duty cycle

In 100 and 200-Gb/s transmissions, PDM-(D)QPSK

signals carry 50 and 100-Gb/s per polarization,

respectively (Fig. 1). According to Peter J. Winzer in

[28], IFWM predominates in SSMF spans whereas

IXPM appears in NZDSF+ spans with bit rates ranging

between 50 and 100-Gb/s per polarization. However, the

presence of both nonlinearities does not only depend on

the optical fiber type, but also the duty cycle value must

be taken into account.

A priori, IFWM prevails over IXPM in high

dispersion fibers. This is mainly valid with low duty

cycles (33% ‒ 50%), but if we set up the optical carrier

with a higher duty cycle value (67% ‒ 100%) the

stimulation of IXPM will increase, i.e. IXPM is

proportional to the duty cycle value. Obviously, the pulse

overlapping is more pronounced with a higher duty cycle

and consequently the phase is more distorted by the

amplitude fluctuations of adjacent pulses. In this

situation, the eye diagram is closed by amplitude jitter

(associated with the presence of ghost pulses generated

by IFWM) and phase jitter (due to NPN generated by

IXPM). Therefore, IXPM cannot be ignored in SSMF

spans for the PDM-NRZ-(D)QPSK and PDM-67%RZ-

(D)QPSK signals (Fig. 10.a).

On the other hand, the differences are not so

pronounced in low dispersion fibers for different duty

cycle values (Fig. 10.b). In these fibers, PDM-(D)QPSK

signals are affected by both intrachannel nonlinearities,

without a clear predominance of any of them. For low

duty cycles, IFWM is slightly lower than IXPM, so the

phase jitter is the main cause of the eye diagram

degradation. Meanwhile, IFWM increases with the duty

cycle value and puts on the same level as IXPM. In that

case, the eye diagram is affected by amplitude and phase

jitter.

In general, a high duty cycle value favors the

presence of both intrachannel nonlinearities, whereas the

GVD coefficient is fundamental to determine the

predominant nonlinearity when a low duty cycle is

employed: IFWM in SSMF and IXPM in NZDSF+.

8 Conclusions

The amount of traffic carried on optical backbone

networks has been growing exponentially over the past

two decades. Nowadays, the required capacity on each

DWDM channel ranges between 100 and 200-Gb/s. In

2012, the ITU-T recommended the use of “Flexible-

Grids” networks enabling the possibility to continue

working with the PDM-(D)QPSK format beyond 100-G,

due to the current technological difficulties to achieve

long-haul data communications with the multilevel

PDM-16-QAM format, mainly focused on short-reach

transmissions.

An intensive analysis has been made of polarization-

division multiplexed quadrature phase shift keying

modulation formats in 100 and 200-Gb/s DWDM

systems. The performance offered by PDM-(D)QPSK

varies according to the line code that is employed to

carve the pulses of the optical carrier: NRZ, 33% RZ,

50% RZ, 67% RZ or CSRZ. Each option offers different

tolerances to linear and nonlinear impairments of a

lightpath. The features of PDM-(D)QPSK have been

characterized measuring the robustness to ASE noise,

Fig. 10. Eye diagrams of PDM-33%RZ-(D)QPSK (left) and PDM-NRZ-(D)QPSK (right). The distortion induced by IXPM and IFWM

results in timing and amplitude jitter, respectively.

crosstalk, optical filtering, chromatic dispersion,

polarization mode dispersion and intrachannel

nonlinearities.

PDM-33%RZ-(D)QPSK reveals an enormous

resistance against the ghost pulses generated by IFWM

and the phase fluctuations of IXPM, but the handicap of

this signal is its low SE in DWDM systems, 1 b/s/Hz.

Thanks to its great tolerance to filtering distortion, the SE

may be increased from 1 to 2 b/s/Hz in DWDM systems

prefiltering this format in the TX and allowing its

integration in the grids of 50 and 100 GHz for 100 and

200 Gb/s transmissions, respectively. In this way, it is

possible to exploit the great advantage of RZ pulses with

low duty cycle: the reduction of pulse-to-pulse

interaction. This feature allows to increase the tolerance

to CD, PMD and intrachannel nonlinearities. In contrast,

the PDM-NRZ-(D)QPSK format has a slightly higher SE

than the other options and it shows better tolerance to

filtering distortion and chromatic dispersion in filterless

networks.

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